Foreign Currency Billing in Projects

We currently have a requirement in our USD set of books to bill in EUR (or any other currency).  What's the best approach with the setups using native Project Billing.

Since billing was the only requirement, we tried enabling multi-currency billing on a USD project.  However, we ran into rounding issues even if our bill rate schedule is an even amount.  For example even if I have an EUR bill rate schedule of Joe @ 100 EUR per HR, the bill amounts sometimes come out as 100.01.  For cost plus projects where it uses a burden schedule, Oracle's taking the USD cost * multiplier * currency rate = Bill Amt which won't work for us.  Therefore, I don't think that's an option based on some simple tests.